The aim of this paper is to study the effect of relaxing the assumption in the Peierls
analysis that the dislocation must be wide compared to the atom spacing. To do this the use of the
continuum description of the in-plane strains caused by the presence of an edge dislocation is
replaced by an atomistic interaction taken to be linear elastic. It is found that in this case the inplane
interactions give a contribution to the overall misfit energy changes that are not present in the
Peierls analysis because of the use of a continuum approach. This contribution modifies these
energy changes so that the total misfit energy is a minimum at the conventional low energy
positions (whereas in the Peierls analysis it is a maximum) and gives values of the Peierls stress in
reasonable agreement with those measured.